Many different systems perform or implement multi-dimensional non-linear multivariable processes. The systems are “non-linear” in that one or more outputs of the system do not respond linearly to changes in one or more inputs of the system. The systems are “multivariable” in that multiple inputs of the system can be used to make adjustments to one or more outputs of the system. The systems are “multi-dimensional” in that they have multiple dimensions, such as a spatial dimension and a temporal dimension.
Ideally, the behavior of these types of processes could be simulated, which could be done to support a wide variety of functions. For example, these simulations could be done for in-house validation of new control systems, realistic customer acceptance tests, system checkouts, and training of machine operators and process engineers. However, there are several problems with designing or configuring a multi-dimensional non-linear multivariable process simulator. For example, it is often very expensive to derive the non-linear dynamic and spatial process models that represent a multi-dimensional non-linear multivariable process. Also, the resulting set of non-linear differential equations or partial differential equations representing a multi-dimensional non-linear multivariable process can be very time consuming to solve, often rendering them unsuitable for real-time use.
As a particular example, various systems are available and used to manufacture sheets of paper or other sheet products. These types of sheet-making systems are non-linear in that changes to various manipulated variables (such as an amount of drying applied to the sheet) result in non-linear changes to one or more controlled variables (such as moisture of the sheet). These types of sheet-making systems are multivariable in that multiple manipulated variables can be analyzed and used to adjust one or more controlled variables. The spatial and temporal dimensions in this example correspond to the cross direction (CD) and machine direction (MD) of a paper machine. In the context of a paper making process, “spatial” and “cross direction” can be used interchangeably. Also, “temporal,” “dynamic,” and “machine direction” can be used interchangeably.
Prior techniques for simulating the behaviors of these types of sheet-making systems have often involved separate linear multivariable CD and linear multivariable MD simulators. Some techniques also provided for the ability to simulate the behavior of low-level controllers in the sheet-making systems. However, these prior techniques often lacked any mechanism for simulating the behavior of MD or CD actuators, simulating the effects of a scanning set of sensors, and simulating different types of MD and CD disturbances. These prior techniques also often lacked any mechanism for simulating non-linear characteristics of a process in real time.